Title:	A quantum kinematics for asymptotically flat gravity
Authors:	Campiglia, Miguel Varadarajan, Madhavan
Issue Date:	9-Jul-2015
Publisher:	IOP Publishing Ltd.
Citation:	Classical and Quantum Gravity, 2015, Vol.32, p135011
Abstract:	We construct a quantum kinematics for asymptotically flat gravity based on the Koslowski–Sahlmann (KS) representation. The KS representation is a generalization of the representation underlying loop quantum gravity (LQG) which supports, in addition to the usual LQG operators, the action of 'background exponential operators', which are connection dependent operators labelled by 'background' su(2) electric fields. KS states have, in addition to the LQG state label corresponding to one dimensional excitations of the triad, a label corresponding to a 'background' electric field that describes three dimensional excitations of the triad. Asymptotic behaviour in quantum theory is controlled through asymptotic conditions on the background electric fields that label the states and the background electric fields that label the operators. Asymptotic conditions on the triad are imposed as conditions on the background electric field state label while confining the LQG spin net graph labels to compact sets. We show that KS states can be realised as wave functions on a quantum configuration space of generalized connections and that the asymptotic behaviour of each such generalized connection is determined by that of the background electric fields which label the background exponential operators. Similar to the spatially compact case, the Gauss law and diffeomorphism constraints are then imposed through group averaging techniques to obtain a large sector of gauge invariant states. It is shown that this sector supports a unitary action of the group of asymptotic rotations and translations and that, as anticipated by Friedman and Sorkin, for appropriate spatial topology, this sector contains states that display fermionic behaviour under $2\pi $ rotations
Description:	Open Access
URI:	http://hdl.handle.net/2289/6299
ISSN:	0264-9381 1361-6382 (online)
Alternative Location:	http://arxiv.org/abs/1412.5527 http://dx.doi.org/10.1088/0264-9381/32/13/135011 http://adsabs.harvard.edu/abs/2015CQGra..32m5011C
Copyright:	2015 IOP Publishing Ltd.
Appears in Collections:	Research Papers (TP)

Items in RRI Digital Repository are protected by copyright, with all rights reserved, unless otherwise indicated.